Mutual inductor transient waveform full-bandwidth reduction method and system

Abstract

The invention relates to the technical field of power system relay protection, discloses a transformer transient waveform full-bandwidth reduction method and system, and aims to accurately represent amplitude-frequency characteristics and bandwidth limitation of a transformer by constructing a frequency domain transfer function model of the transformer. After a time domain waveform collected by a mutual inductor is converted into broadband frequency domain information, inverse operation is carried out on the broadband frequency domain information and a transfer function model subjected to regularization processing, signal attenuation outside an effective bandwidth is compensated, high-frequency and low-frequency transient components filtered or distorted by hardware are recovered, and therefore the bandwidth bottleneck of a physical sensor is broken through. And then, carrying out inverse transformation on the compensated broadband frequency domain information to obtain a high-fidelity reduced time domain waveform signal. The waveform signal is closer to a real fault signal in the aspects of shape, amplitude and transient characteristic time sequence, the problem that full-bandwidth effective detection is difficult to realize in the process of detecting the fault waveform by using a mutual inductor is solved, and an accurate data basis is provided for subsequent fault identification and traceability analysis thereof.

Description

Technical Field

[0001] This invention relates to the field of power system relay protection technology, specifically to the field of fault waveform restoration methods for high voltage direct current transmission systems, and particularly to a method and system for restoring the full bandwidth of transient waveforms of instrument transformers based on inverse transfer function operation and regularization. Background Technology

[0002] DC transmission is a crucial carrier for inter-regional energy interconnection, but its fault transient processes are extremely fast, have a wide spectrum, and involve large amounts of energy. However, DC transmission systems are characterized by high operating voltage levels and concentrated energy transmission, leading to frequent faults such as commutation failures and line short circuits, with the fault process exhibiting significant rapid transient characteristics. The entire fault transient process may last only a few hundred microseconds, during which the fault waveform spectrum is broad and contains enormous energy, making it extremely destructive. Therefore, DC transmission systems require extremely high accuracy in fault diagnosis and reliability in protection actions. Furthermore, the complete and accurate capture of fault transient waveforms is a core prerequisite for achieving efficient fault diagnosis and reliable protection, and is crucial for preventing the expansion of the fault range, reducing the risk of damage to critical equipment, and ensuring the safe and stable operation of the large power grid.

[0003] To address this challenge, the mainstream broadband fault waveform monitoring methods in the field are currently divided into three categories: non-contact capacitive coupling sensors, optical transformers, and RC voltage divider transformers.

[0004] (1) Non-contact capacitive coupling sensor calculates the line potential by inverting the parasitic capacitance between the capacitive probe and the line. However, its parasitic capacitance value is related to the installation position of the probe and is difficult to determine accurately. While restricting the frequency response characteristics, it also lacks key parameters such as amplitude, resulting in poor fidelity when restoring transient fault waveforms containing rich high-frequency components.

[0005] (2) Optical transformers utilize the physical effects of materials with electro-optic properties to modulate voltage signals onto optical wave properties for sensing. Although this method has the potential for wide bandwidth, the sensing head needs to integrate a complex optical crystal and lens system and perform precise collimation. Its electro-optic coefficient is easily affected by ambient temperature and humidity, resulting in unstable probe response characteristics and ultimately causing measurement waveform distortion and errors.

[0006] (3) The RC voltage divider transformer is currently the most important measurement method in DC transmission systems. It uses a precisely configured network of resistors and capacitors and the voltage divider principle to linearly convert the wide-bandwidth, high-amplitude primary voltage / current signal generated during fault transients into a standard secondary low-level signal that can be received by the acquisition equipment. Due to the inherent frequency characteristics of the primary voltage divider circuit, secondary voltage divider circuit, and stray parameters inside the transformer, its effective operating bandwidth is limited to a limited range. However, the DC fault transient signal spectrum is extremely wide, including both the extremely high-frequency components generated in the early stage of insulation breakdown and the low-frequency components during energy decay. The limited bandwidth makes it impossible for the transformer to simultaneously capture and transmit these two key frequency components without distortion, resulting in severe distortion of the output fault waveform, such as smoothing of high-frequency oscillations or attenuation of low-frequency components.

[0007] It is evident that for waveform detection in DC transmission line detection scenarios, as well as other scenarios such as line external insulation breakdown discharge and lightning electric fields, especially for the mainstream RC voltage divider transformer, there is a core bottleneck of insufficient operating bandwidth when facing the high-precision and wide-bandwidth monitoring requirements of DC fault transient waveforms. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a method and system for full-bandwidth restoration of transient waveforms of current transformers, which can overcome the difficulty of achieving effective full-bandwidth detection in the process of using current transformers to detect fault waveforms.

[0009] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for full-bandwidth restoration of transient waveforms of a current transformer, comprising the following steps: S1. Construct the frequency domain transfer function model of the current transformer; S2. Obtain the original time-domain waveform signal sensed by the current transformer, and convert the original time-domain waveform signal, either directly or after preprocessing, into frequency-domain feature information through fast Fourier transform. S3. Introduce a regularization parameter into the frequency domain transfer function model to obtain a numerically stable frequency domain transfer function model; perform inverse operation on the frequency domain feature information and the numerically stable frequency domain transfer function model through frequency domain division to obtain wideband frequency domain information; S4. Perform an inverse fast Fourier transform on the wideband frequency domain information to obtain the time-domain waveform signal with bandwidth restored.

[0010] Preferably, step S1 includes: based on the topology of the mutual inductor, determining the frequency domain transfer function of each subsystem in the topology through Laplace transform, multiplying the transfer functions of each connected subsystem to obtain the overall frequency domain transfer function model of the mutual inductor.

[0011] Preferably, the current transformer is configured as a capacitive-resistive voltage divider current transformer, which includes a primary circuit and a secondary circuit; the primary circuit includes a first high-voltage arm composed of a first resistor and a first capacitor connected in parallel, and a first low-voltage arm composed of a second resistor and a second capacitor connected in parallel; the first high-voltage arm and the first low-voltage arm are connected in series between the first high-voltage input terminal and ground, and the voltage is extracted from both ends of the first low-voltage arm and used as the output of the primary circuit; The frequency domain transfer function of the primary loop for: , in, The capacitance value of the first capacitor is... This is the capacitance value of the second capacitor. This is the resistance value of the first resistor. This is the resistance value of the second resistor. The voltage being measured. This refers to the output voltage of the primary circuit. The secondary circuit includes a second high-voltage arm consisting of a third resistor and a third capacitor connected in parallel, and a second high-voltage arm consisting of a fourth resistor; the second high-voltage arm and the second low-voltage arm are connected in series across the two ends of the first low-voltage arm, and the voltage is extracted from the two ends of the second low-voltage arm and used as the output of the secondary circuit. The frequency domain transfer function of the secondary circuit is: , in, This is the capacitance value of the third capacitor. This is the resistance value of the third resistor. This is the resistance value of the fourth resistor. This is the input voltage of the secondary circuit. This is the output voltage of the secondary circuit.

[0012] Preferably, the capacitive-resistive voltage divider transformer further includes an isolation circuit; The isolation circuit includes an operational amplifier, a fifth resistor, a sixth resistor, and a fourth capacitor. The fifth resistor is connected in series between the inverting input of the operational amplifier and the input of the isolation circuit. The sixth resistor and the fourth capacitor are connected in parallel between the inverting input of the operational amplifier and the output of the isolation circuit. The high and low voltage ends of the second low-voltage arm are connected sequentially to the input terminal of the isolation circuit and the non-inverting input terminal of the operational amplifier, respectively. The transfer function of the isolation circuit for: , in, This is the capacitance value of the fourth capacitor. This is the resistance value of the fifth resistor. This is the resistance value of the sixth resistor; The frequency domain transfer function model for: .

[0013] Preferably, the processed original time-domain waveform signal includes the following steps: sampling the time-domain waveform signal at a preset sampling frequency to obtain discrete sequence data; multiplying the discrete sequence data with a window function point by point to obtain a windowed signal; and performing a fast Fourier transform on the windowed signal to obtain frequency domain feature information.

[0014] Preferably, the original time-domain waveform signal is sampled at a sampling frequency. This can be converted into the following discrete sequence: , in, The sampling period is the sampling frequency. The reciprocal, The index is the sequence number of the discrete sequence data.

[0015] The window function is a Hanning-Hamming hybrid window: , in, For window functions, For window function coefficients; The windowed signal Determined by the following formula: ,in, This is the amplitude correction coefficient.

[0016] Preferably, the integral of the continuous-time Fourier transform over the windowed signal is decomposed into the sum of the areas of an infinite number of narrow rectangles, and the windowed signal within a preset length is subjected to a fast Fourier transform to determine the frequency domain feature information.

[0017] Preferably, the frequency domain feature information Determined by the following formula: ,in, For the signal after windowing, The sampling period is The index is the sequence number of the discrete sequence data.

[0018] Preferably, the numerically stabilized frequency domain transfer function model for: , in, For the constructed frequency domain transfer function model, For regularization parameters; The wideband frequency domain information Determined by the following formula: ,in, This refers to frequency domain feature information.

[0019] In a second aspect, the present invention provides a transducer transient waveform full bandwidth restoration system for implementing the above-described transducer transient waveform full bandwidth restoration method.

[0020] Compared with existing technologies, the present invention provides a method and system for full bandwidth restoration of transient waveforms of current transformers, which has the following advantages:

[0021] (1) This invention constructs a frequency domain transfer function model to fully describe the amplitude-frequency characteristics of the transformer and the waveform data of input and response, and clarifies its effective working bandwidth and out-of-band attenuation characteristics. By converting the original time-domain waveform signal sensed by the transformer into frequency domain feature information, and by performing inverse operation with the frequency domain feature information and the regularized frequency domain transfer function model, it achieves accurate gain compensation for the frequency band outside the effective bandwidth of the transformer in the frequency domain with the help of the transfer function, and recovers the high-frequency and low-frequency transient components that are filtered out or distorted by the transformer. This makes the final effective observation bandwidth no longer limited by the inherent characteristics of the physical sensor, thereby breaking through the physical bandwidth bottleneck of the sensing hardware.

[0022] (2) The present invention performs inverse transformation on the wideband frequency domain information obtained by gain compensation to obtain the time domain waveform signal with bandwidth restoration. The restored time domain waveform signal is closer to the real original time domain waveform signal in terms of waveform shape, amplitude, and timing relationship of key transient features. The high-fidelity transient time domain waveform signal contains complete spectrum information of the fault, which significantly improves the fidelity and accuracy of the restoration of the transient waveform, and provides a high-fidelity data foundation for subsequent fault identification and source tracing analysis.

[0023] (3) In the inverse operation, the present invention introduces a regularization parameter into the frequency domain transfer function model, which avoids the problem that the measurement noise is amplified sharply when the sensor responds to the weak frequency band during division. Moreover, it can stably and reliably process real measurement signals containing noise, thereby enhancing the robustness of the algorithm and the practicality of fault detection. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a method for restoring the full bandwidth of transient waveforms of a current transformer according to an embodiment of the present invention.

[0025] Figure 2 This is the topology of the primary circuit of a capacitive-resistive voltage divider transformer according to an embodiment of the present invention.

[0026] Figure 3 This is the topology of the secondary circuit of a capacitive-resistive voltage divider transformer according to an embodiment of the present invention.

[0027] Figure 4 This describes the topology of the isolation circuit for a capacitive-resistive voltage divider transformer according to an embodiment of the present invention.

[0028] Figure 5 This is a graph showing the amplitude-frequency characteristic of a capacitive-resistive voltage divider transformer according to an embodiment of the present invention.

[0029] Figure 6 This is a comparison diagram of the primary high-voltage side input voltage and the transformer output waveform according to an embodiment of the present invention.

[0030] Figure 7 This is a comparison diagram of the original fault waveform and the time-domain waveform signal restored by bandwidth according to an embodiment of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Example 1

[0032] like Figure 1 The diagram illustrates a method for restoring the full bandwidth of a current transformer transient waveform according to Embodiment 1 of the present invention. This method includes the following steps: S1. Construct the frequency domain transfer function model of the current transformer. Step S1 constructs an accurate transfer function model for the current transformer, which fully describes the amplitude-frequency and phase-frequency characteristics of the current transformer and clarifies its effective operating bandwidth and out-of-band attenuation characteristics.

[0033] S2. Obtain the original time-domain waveform signal sensed by the current transformer, and convert the original time-domain waveform signal, either directly or after preprocessing, into frequency-domain feature information through fast Fourier transform.

[0034] S3. Introduce a regularization parameter into the frequency domain transfer function model to obtain a numerically stable frequency domain transfer function model; perform inverse operation on the frequency domain feature information and the numerically stable frequency domain transfer function model through frequency domain division to obtain wideband frequency domain information.

[0035] Steps S2 and S3 involve, on the one hand, extracting frequency domain feature information from the original time-domain waveform signal to achieve a frequency domain representation of the distorted waveform. On the other hand, a regularization parameter is introduced into the frequency domain transfer function model to stabilize the numerical value of the transfer function and solve the problem of drastically amplifying weak frequency band noise during inverse operations. Finally, inverse operations are performed by dividing the frequency domain feature information and the frequency domain transfer function model in the frequency domain to obtain the preliminary compensated wideband frequency domain information.

[0036] S4. Perform an inverse fast Fourier transform on the wideband frequency domain information to obtain the time-domain waveform signal with bandwidth restoration. Step S4 restores the compensated wideband frequency domain information to a time-domain waveform signal. Subsequent use of this high-fidelity full-bandwidth time-domain waveform signal for fault diagnosis and analysis will greatly improve the accuracy and reliability of detection.

[0037] Therefore, this invention overcomes the difficulty of achieving effective full-bandwidth detection in the process of detecting fault waveforms using current transformers, and realizes the full-bandwidth, high-fidelity and high-accuracy restoration of transient waveforms of current transformers. Example 2

[0038] This embodiment is a method for restoring the full bandwidth of transient waveforms of a capacitive-resistive voltage divider transformer according to Embodiment 2 of the present invention, and is a further specific embodiment based on Embodiment 1. The method of this embodiment is specifically used for restoring the full bandwidth of transient waveforms of a capacitive-resistive voltage divider transformer.

[0039] This embodiment of a method for restoring the full bandwidth of transient waveforms of a capacitive-resistive voltage divider transformer includes the following steps: S10. Based on the topology of the capacitive-resistive voltage divider transformer, the frequency domain transfer function of each subsystem in the topology is determined by the Laplace transform. The transfer functions of each series of subsystems are multiplied to obtain the overall frequency domain transfer function model of the capacitive-resistive voltage divider transformer. S20. Obtain the original time-domain waveform signal sensed by the capacitive-resistive voltage divider transformer, sample the time-domain waveform signal at a preset sampling frequency to obtain discrete sequence data; multiply the discrete sequence data with a window function point by point to obtain the windowed signal; decompose the integral of the continuous-time Fourier transform on the windowed signal into the sum of the areas of an infinite number of narrow rectangles, and determine the frequency domain feature information by performing a fast Fourier transform on the windowed signal within a preset length. S30. Introduce a regularization parameter into the frequency domain transfer function model to obtain a numerically stable frequency domain transfer function model; perform inverse operation on the frequency domain feature information and the numerically stable frequency domain transfer function model through frequency domain division to obtain wideband frequency domain information; S40. Perform an inverse fast Fourier transform on the wideband frequency domain information to obtain the time-domain waveform signal with bandwidth restored.

[0040] like Figures 2 to 4 The image shows a capacitive-resistive voltage divider transformer according to this embodiment. The capacitive-resistive voltage divider transformer includes a primary circuit, a secondary circuit, and an isolation circuit.

[0041] refer to Figure 2 The primary circuit includes a first high-voltage arm consisting of a first resistor and a first capacitor connected in parallel, and a first low-voltage arm consisting of a second resistor and a second capacitor connected in parallel. The first high-voltage arm and the first low-voltage arm are connected in series between the first high-voltage input terminal and ground. The voltage is extracted from both ends of the first low-voltage arm and used as the output of the primary circuit.

[0042] In this embodiment, step S10 specifically involves analyzing the topology of the primary voltage divider circuit to obtain the relationship between the output voltage of the first low-voltage arm and the input voltage of the first high-voltage arm: , in, The capacitance value of the first capacitor is... This is the capacitance value of the second capacitor. This is the resistance value of the first resistor. This is the resistance value of the second resistor. The voltage being measured. This is the output voltage of the primary circuit.

[0043] After obtaining the time-domain transformation relationship between the measured voltage and the output voltage of the primary voltage divider circuit, a Laplace transform is performed on this relationship to obtain the frequency-domain transfer function of the primary circuit. : .

[0044] refer to Figure 3 The secondary circuit includes a second high-voltage arm composed of a third resistor and a third capacitor connected in parallel, and a second high-voltage arm composed of a fourth resistor. The second high-voltage arm and the second low-voltage arm are connected in series across the two ends of the first low-voltage arm. The voltage is extracted from the two ends of the second low-voltage arm and used as the output of the secondary circuit. Analyzing the topology of the capacitive-resistive voltage divider transformer's secondary circuit, the relationship between the low-voltage side output voltage and the high-voltage side input voltage can be obtained as follows: , in, This is the capacitance value of the third capacitor. This is the resistance value of the third resistor. This is the resistance value of the fourth resistor. This is the input voltage of the secondary circuit. This is the output voltage of the secondary circuit.

[0045] After obtaining the time-domain transformation relationship between the primary circuit output voltage and the secondary voltage divider circuit output voltage, a Laplace transform is performed on this relationship to obtain the frequency-domain transfer function of the secondary circuit. : .

[0046] In addition to the primary and secondary circuits, capacitive-resistive voltage divider transformers usually have an isolation amplifier added before the output terminal to prevent excessively high output voltage from damaging the subsequent data acquisition and monitoring section. The operational amplifier circuit is used to limit the output voltage to achieve electrical isolation between the primary and secondary sides.

[0047] refer to Figure 4 The isolation circuit includes an operational amplifier, a fifth resistor, a sixth resistor, and a fourth capacitor. The fifth resistor is connected in series between the inverting input of the operational amplifier and the input of the isolation circuit. The sixth resistor and the fourth capacitor are connected in parallel between the inverting input of the operational amplifier and the output of the isolation circuit.

[0048] Based on the analysis of the operational amplifier characteristics, the transfer function of the isolation circuit can be obtained. : , in, This is the capacitance value of the fourth capacitor. This is the resistance value of the fifth resistor. This is the resistance value of the sixth resistor.

[0049] Calculate the overall frequency domain transfer function model of the capacitive-resistive voltage divider transformer: Connect the circuit topologies obtained from the previous steps to obtain the overall frequency domain transfer function model of the capacitive-resistive voltage divider transformer. The product of the transfer functions of each part is: , .

[0050] For ease of understanding, in one example of this embodiment, the resistance of the first resistor R1 is 200MΩ, the resistance of the second resistor R2 is 27.65kΩ, the resistance of the third resistor R3 is 650kΩ, the resistance of the fourth resistor R4 is 35kΩ, the resistances of the fifth and sixth resistors R5 and R6 are 500Ω, the capacitance of the first capacitor C1 is 400pF, the capacitance of the second capacitor C2 is 3200nF, the capacitance of the third capacitor C3 is 270pF, and the capacitance of the fourth capacitor C4 is 10pF. (Reference) Figure 5 This is the amplitude-frequency characteristic curve of the overall frequency domain transfer function model constructed from the capacitive-resistive voltage divider transformer in this example. (Reference) Figure 6When an overvoltage waveform is input to the capacitive-resistive voltage divider transformer in this example, the corresponding output waveform will be obtained. As can be seen from the comparison in the figure below, the bandwidth limitation of each structure of the transformer causes the waveform signal to be distorted and cannot retain all the characteristics.

[0051] This concludes step 10. The physical basis of this step is that the characteristics of any linear time-invariant (LVM) system in the frequency domain can be fully described by its transfer function. By analyzing its specific circuit topology (the values ​​and connections of resistors and capacitors), differential equations relating its input and output can be established based on Kirchhoff's laws. Subsequently, the time-domain differential equations are transformed into concise algebraic equations in the complex frequency domain (s-domain) using Laplace transform, thus obtaining the frequency domain transfer functions of each subsystem. The overall system response is the superposition of the responses of each cascaded subsystem; therefore, the overall transfer function is the product of the transfer functions of each subsystem. Based on step S10, the transfer function and amplitude-frequency characteristics of the capacitive-resistive voltage divider transformer, as well as the input and response waveform data, are obtained.

[0052] In this embodiment, step S20 specifically involves sampling the original time-domain waveform signal according to the sampling frequency. This can be converted into the following discrete sequence: , in, The sampling period is the sampling frequency. The reciprocal, The index is the sequence number of the discrete sequence data.

[0053] The window function is a Hanning-Hamming hybrid window: , in, For window functions, These are the coefficients of the window function.

[0054] By selecting appropriate Parameters such as α=0.52, β=0.48, and γ=0.02 are used to obtain a windowing function suitable for the output waveform of the current transformer. Then, point-by-point multiplication is performed to apply the window, resulting in the windowed signal. Determined by the following formula: ,in, This is the amplitude correction coefficient.

[0055] It is worth noting that, The amplitude correction coefficient is used to compensate for signal amplitude attenuation caused by windowing. For the Hanning-Hamming hybrid window, Take the amplitude correction coefficient as The reciprocal of the window function coefficients. For example, if α = 0.52, then... .

[0056] Based on the principle of continuous-time Fourier transform, the integral of the continuous-time Fourier transform over the windowed signal is decomposed into the sum of the areas of an infinite number of narrow rectangles, as shown in the following formula: .

[0057] To simplify calculations, only the windowed signal within a preset length is subjected to a Fast Fourier Transform (FFT), meaning n has a value between 0 and N-1. The summation range is simplified to 0 to N-1 to determine the frequency domain feature information. The frequency domain feature information... Determined by the following formula:

[0058] ,in, For the signal after windowing, The sampling period is The index is the sequence number of the discrete sequence data.

[0059] Step S20 concludes here. The original time-domain waveform signal is an analog signal, which is sampled at a preset frequency and digitized to obtain discrete sequence data suitable for further processing. Windowing the discrete sequence data helps prevent spectral leakage during Fast Fourier Transform (FFT). The Hanning-Hamming hybrid window is used by adjusting its construction parameters. This allows the complex transient original time-domain waveform signal to contain both critical high-frequency oscillations that determine the fault type and weak frequency components that are easily overwhelmed by leakage energy. Balancing leakage suppression with signal distortion provides a higher-quality initial spectrum for subsequent inverse transfer function operations. The continuous-time Fourier transform (FTFT) is an integral of a continuous signal, which is computationally difficult. However, by decomposing the integral into the sum of the areas of an infinite number of narrow rectangles, the FTFT can be used to solve it. Inputting a windowed signal into the FTFT outputs a complex sequence, representing the frequency domain characteristic information. By using the S20 method, the frequency domain characteristic information of the waveform can be calculated based on the time domain waveform signal of the waveform to be restored.

[0060] In this embodiment, step S30 specifically involves, before performing frequency domain calculations on the signal, to prevent... At certain frequency points, the noise term is very small or zero, which can amplify the noise and cause the time-domain results to diverge or ring severely. Therefore, stabilization is required in the denominator. The numerically stabilized frequency-domain transfer function model is described in this context. for: , in, For the constructed frequency domain transfer function model, For regularization parameters; Ringing effects can be suppressed by selecting appropriate regularization parameters. Specifically, a small quantity is added to the denominator of the transfer function to prevent numerical instability when the denominator is zero or close to zero. For example, this can be achieved by... Sure.

[0061] Based on the frequency domain transfer function model of the capacitive-resistive voltage divider transformer obtained in S10 and the frequency domain characteristic information of the output waveform obtained in S2, inverse calculation is performed through frequency domain division to deduce the frequency domain information of the original time-domain waveform signal. The wideband frequency domain information... Determined by the following formula: ,in, This refers to frequency domain feature information.

[0062] This step can recover signal components outside the current transformer bandwidth, achieving an initial correction of bandwidth-limited distortion.

[0063] In this embodiment, step S40 specifically involves performing an N-point inverse fast Fourier transform based on the frequency domain information of the original time-domain waveform signal obtained through reverse engineering, converting the wideband frequency domain information into a time-domain waveform signal with restored bandwidth. ,Right now: , Where t=n / fs (n=0,1,…,N-1) represents the discrete time in the time domain.

[0064] This concludes step S40.

[0065] like Figure 7 As shown, the method in this embodiment can yield an approximate reverse-engineering result of the full-bandwidth fault waveform. (Comparison) Figure 6 It can be seen that, compared with the voltage directly output by the transformer, the wideband frequency domain information converted into the time domain waveform signal after bandwidth restoration is closer to the transient fault waveform of the input transformer, providing a high-fidelity data foundation for subsequent fault identification and source tracing analysis.

[0066] According to embodiments of the present invention, a system for restoring the full bandwidth of transient waveforms of a current transformer also relates. This system is used to implement the method for restoring the full bandwidth of transient waveforms of a current transformer as described in the above embodiments.

[0067] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method of mutual inductor transient waveform full bandwidth restoration, characterized by, The method comprises the following steps: S1, constructing a frequency domain transfer function model of the transformer; S2, obtaining an original time domain waveform signal sensed by the transformer, and converting the original time domain waveform signal in a direct manner or after preprocessing into frequency domain feature information through fast Fourier transform; S3, introducing a regularization parameter into the frequency domain transfer function model to obtain a numerically stable frequency domain transfer function model; and performing inverse operation on the frequency domain feature information and the numerically stable frequency domain transfer function model through frequency domain division to obtain wideband frequency domain information; S4, performing inverse fast Fourier transform on the wideband frequency domain information to obtain a bandwidth-restored time domain waveform signal.

2. The method of claim 1, wherein, The step S1 comprises: determining frequency domain transfer functions of each subsystem in a topology structure of the transformer through Laplace transform based on the topology structure of the transformer, multiplying the transfer functions of each cascaded subsystem to obtain the frequency domain transfer function model of the whole transformer.

3. The method of claim 2, wherein, The transformer is configured as a capacitance-resistance voltage divider type transformer, the capacitance-resistance voltage divider type transformer comprises a primary circuit and a secondary circuit; the primary circuit comprises a first high-voltage arm composed of a first resistor and a first capacitor in parallel, and a first low-voltage arm composed of a second resistor and a second capacitor in parallel; the first high-voltage arm and the first low-voltage arm are connected in series between a first high-voltage input end and the ground, and a divided voltage extracted at both ends of the first low-voltage arm is taken as an output of the primary circuit; The frequency domain transfer function of the primary circuit is: is: ， wherein, C1 is a capacitance value of the first capacitor, C2 is a capacitance value of the second capacitor, R1 is a resistance value of the first resistor, R2 is a resistance value of the second resistor, V is a measured voltage, Vo is an output voltage of the primary circuit; The secondary circuit comprises a second high-voltage arm composed of a third resistor and a third capacitor in parallel, and a second low-voltage arm composed of a fourth resistor; the second high-voltage arm and the second low-voltage arm are connected in series at both ends of the first low-voltage arm, and a divided voltage extracted at both ends of the second low-voltage arm is taken as an output of the secondary circuit; The frequency domain transfer function of the secondary circuit is: ， wherein, is a capacitance value of the third capacitor, is a resistance value of the third resistor, is a resistance value of the fourth resistor, is an input voltage of the secondary circuit, is an output voltage of the secondary circuit.

4. The method of claim 2, wherein, The capacitance-resistance voltage divider type transformer further comprises an isolation circuit; The isolation circuit comprises an operational amplifier, a fifth resistor, a sixth resistor and a fourth capacitor, the fifth resistor is connected in series between the inverting input end of the operational amplifier and the input end of the isolation circuit, and the sixth resistor and the fourth capacitor are connected in parallel between the inverting input end of the operational amplifier and the output end of the isolation circuit; The high-voltage end and the low-voltage end of the second low-voltage arm are connected to the input end of the isolation circuit and the non-inverting input end of the operational amplifier, respectively; Transfer function of the isolation circuit is: ， wherein, C4 is a capacitance value of a fourth capacitor, R5 is a resistance value of a fifth resistor, R6 is a resistance value of a sixth resistor; The frequency domain transfer function model is: .

5. The method of claim 1, wherein, The processed original time domain waveform signal comprises the following steps: sampling the time domain waveform signal at a preset sampling frequency to obtain discrete sequence data; multiplying the discrete sequence data with a window function point by point to obtain a windowed signal; and performing fast Fourier transform on the windowed signal to obtain frequency domain feature information.

6. The transformer transient waveform full-bandwidth restoration method of claim 5, wherein the window function is a Hanning-Hamming hybrid window: sampling the original time domain waveform signal at a sampling frequency into a discrete sequence as follows: ， wherein is the sampling period, is the inverse of the sampling frequency is the index of the discrete sequence data;​ The integral of the continuous-time Fourier transform on the windowed signal is divided into the sum of infinite narrow rectangular areas, and the windowed signal within a preset length is converted into frequency domain feature information through fast Fourier transform. ， wherein is a window function, is a window function coefficient; the windowed signal is determined by the equation: wherein is an amplitude correction factor.

7. The method of claim 5, wherein, The transformer is used to implement the transformer transient waveform full-bandwidth restoration method of any one of claims 1 to 9.

8. The method of claim 7, wherein, The frequency domain feature information is determined by the following equation: wherein, is the windowed signal, is the sampling period, is the sequence number of the discrete sequence data.

9. The method of claim 1, wherein, The numerically stabilized frequency domain transfer function model is: wherein, for the constructed frequency domain transfer function model, is a regularization parameter; The wideband frequency domain information is determined by the following equation: wherein, is the frequency domain feature information.

10. A transformer transient waveform full bandwidth reduction system characterized by: ​

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